I disagree I don't think that education should be hierarchical with the rich at the top and the working class at the bottom, it should be equal all over with the best teachers spread out so every pupil can be taught the most difficult parts of a subject by the best teachers. This would lead to a fairer society where no one has an advantage over another in any way. That way the working classes might find themselves not only capable of fulfilling the roles that the middle classes think they own and have an exclusive right to but also find themselves doing all the different jobs they dreamed of doing part time.
What people seem to forget is that the public school system is full of oxbridge teachers who graduated with a first class degree and use their friends in oxbridge universities to earmark students for oxbridge long before the pupil has finished his a levels.
The bright disadvantaged pupil from a run down state school is a very small minority compared to the percentage of public school pupils who go on to oxbridge and the percentage of grammar school suckers who get in to oxbridge is presumably high along with well facilitated state schools in nice areas is probably the same. Point is that disadvantaged children do get preferential treatment because they have a lot of potential to succeed at oxbridge. The same as the others have had preferential treatment in the class of education they have received.